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Acta Mathematica Scientia 总被引:1,自引:0,他引:1
1IntroductionLetfibeaboundeddomainOfR"withsmoothboundaryoff,KCL'(fl)xL'(fl)beasubsetdefinedasfollows:K={(yi,yi)EL'(fl)xL'(fl);yi(x) p(yl(x))30,a.e.infi},(1)withwhichisamaximalmonotonegraphonRxR.Whereaisapositiveconstant.Ourmainproblemisasfollows:(O)MinimizeL(y,u)={'[g(y(t)) h(u(t))]at,overallpairssubjecttotheconditionsOurbasichypothesesaboutgandharethefollowing:(H)Bothgandh:L'(fl)~(--co, co]arelowersendcontinuous,convexsproperfunctionals,withg(y)相似文献
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1IntroductionAlotofworkonthesingularlyperturbedboundaryvalueproblemofthirdorderdifferentialequationwereinthecasesofonesmallparameter[1-3].Inthispaper9wediscussthe8ingularperturbationofboundaryvalueproblemforathirdordersemilinearordinarydifferentialequatio… 相似文献
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本文研究具有Robin边界条件的二阶奇异泛函微分方程组A(t,x,x)x=f(t,xt,xt)的两点边值问题,给出该两点边值问题的两个解的先验估计定理和一个解的存在定理. 相似文献
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We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional.For the numerical treatment,we use variational discretization of its Tikhonov regularization:For the state and the adjoint equation,we apply Petrov-Galerkin schemes in time and usual conforming finite elements in space.We prove a-priori estimates for the error between the discretized regularized problem and the limit problem.Since these estimates are not robust if the regularization parameter tends to zero,we establish robust estimates,which--depending on the problem's regularity——enhance the previous ones.In the special case of bang-bang solutions,these estimates are further improved.A numerical example confirms our analytical findings. 相似文献
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EXISTENCEANDNONEXISTENCEOFGLOBALSOLUTIONOFNONLINEARPARABOLICEQUATIONWITHNONLINEARBOUNDARYCONDITION¥WUYONGHUI;WANGMINGXINAbstr... 相似文献
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Chunfang Shen 《应用数学年刊》2018,34(1):71-79
In this paper, we investigate the nonexistence of positive solutions for a class of four-point boundary value problem of nonlinear differential equation with fractional order derivative. We give sufficient conditions on nonlinear term and the parameter such that the boundary value problem has no positive solutions. Some examples are presented to illustrate the main results. 相似文献
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By a fixed point theorem,some new results on the multiplicity of positive solutions to some m-point boundary value problems of second-order functional differential equations are obtained. The associated Green's functions of the problems are also given. 相似文献
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讨论三阶微分方程周期边值问题解的全局结构,其中ρ∈(0,1/3~(1/2))为常数,λ∈R~+=[0,+∞)为参数,f在t=0,t=2π和u=0处有奇异性,关于u处满足次线性增长条件。 相似文献
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四阶方程两点边值问题Hermite有限元解的渐近展式与外推 总被引:1,自引:0,他引:1
1引言有限元解的渐近展式是提高微分方程数值解精度的重要工具,比如亏量校正和外推就是建立在有限元解的渐近展式的基础之上.许多作者对此进行了大量的研究(见[1]-[4]),特别是文[1],提出了在研究有限元解的渐近展式中十分有用的能量嵌入技巧.本文利用能量嵌入定理得到了四阶方程两点边值问题Hermite有限元解及其二阶平均导数的渐近展式,进一步我们还讨论了它们的Richardson外推公式.考虑四阶方程两点边值问题 相似文献
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In this paper,we are concerned with the existence of positive solutions to an m-point boundary value problem with p-Laplacian of nonlinear fractional differential equation.By means of Krasnosel'skii fixed-point theorem on a convex cone and Leggett-Williams fixed-point theorem,the existence results of solutions are obtained. 相似文献
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时变种群扩散系统最优生育率控制的非线性问题 总被引:23,自引:0,他引:23
本文讨论了一类时变种群扩散系统最优生育率控制的非线性问题,证明了最优生育率控制的存在性,给出了控制为最优的必要条件及其最优性组,本结果可为种群扩散系统最优控制问题的实际研究提供物理理论基础。 相似文献
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§1.引言 在实际问题中经常出现带有多个小参数的微分方程问题,例如两参数问题在润滑理论中的应用,在化学反应理论中的应用,以及在直流电动机分析中的应用.从实际问题出发,我们研究几个导数项前乘有不同小参数的微分方程问题.O’Malley对上述问题的渐近方法作了较为深入的研究.[8]中曾探讨带有两个小参数的常微分方程第 相似文献
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C.Clavero 《计算数学(英文版)》1998,(1)
1.IntroductionSingularlyperturbeddifferentialequationsarecharacterizedbythepresenceofasmallparameterEmultiplyingthehighestorderderivatives.Suchproblemsariseinmanyareasofappliedmathematics.Thesolutionsofsingularlyperturbeddifferentialequationstypicallyhave… 相似文献
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本文考虑一类Dirichlet型边界控制半线性抛物型系统,应用半群理论和非线性分析的方法,证明了系统解映射的连续性,给出了系统逼近能控的一个充分条件.对于Neumann型边界控制或混合型边界控制的半线性抛物型系统,可以得到类似的结果. 相似文献
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本文研究了具有点态控制热方程的等价性问题.利用变分法分析时间最优控制的唯一性,能控性以及范数最优控制的特征,获得了具有点态控制约束热方程的时间与范数最优控制问题之间的等价性,推广了现有文献的结果. 相似文献
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Lei Yuan 《计算数学(英文版)》2009,(4):525-542
In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with an integral constraint for the state. We derive the equivalent a posteriori error estimator for the finite element approximation, which particularly suits adaptive multi-meshes to capture different singularities of the control and the state. Numerical examples are presented to demonstrate the efficiency of a posteriori error estimator and to confirm the theoretical results. 相似文献
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An optimal control problem governed by the Stokes equations with L2-norm state constraints is studied.Finite element approximation is constructed.The optimality... 相似文献